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A336066
Numbers k such that the exponent of the highest power of 2 dividing k (A007814) is a divisor of k.
4
2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 42, 44, 46, 48, 50, 52, 54, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 90, 92, 94, 98, 100, 102, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 138, 140, 142, 144
OFFSET
1,1
COMMENTS
All the terms are even by definition.
If m is a term then m*(2*k+1) is a term for all k>=1.
Šalát (1994) proved that the asymptotic density of this sequence is 0.435611... (A336067).
LINKS
Tibor Šalát, On the function a_p, p^a_p(n) || n (n > 1), Mathematica Slovaca, Vol. 44, No. 2 (1994), pp. 143-151.
EXAMPLE
2 is a term since A007814(2) = 1 is a divisor of 2.
MATHEMATICA
Select[Range[2, 150, 2], Divisible[#, IntegerExponent[#, 2]] &]
PROG
(PARI) isok(m) = if (!(m%2), (m % valuation(m, 2)) == 0); \\ Michel Marcus, Jul 08 2020
(Python)
from itertools import count, islice
def A336066_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:n%(~n&n-1).bit_length()==0, count(max(startvalue+startvalue&1, 2), 2))
A336066_list = list(islice(A336066_gen(startvalue=3), 30)) # Chai Wah Wu, Jul 10 2022
CROSSREFS
A001146 and A039956 are subsequences.
Sequence in context: A226295 A090127 A057910 * A120351 A022305 A103799
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 07 2020
STATUS
approved